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How Accurate Are Specific Gravity Calculations?

 

How accurate is specific gravity? There is a quick reference chart below and an SG Scale Precision Checker below that allows you to see how accurate (and inaccurate!) the measurement of SG can be depending on the precision of your scale. The precision of the scale and the weight of the stone being weighed are critical to getting an accurate measurement of specific gravity.

Quick Reference: This chart shows the lightest weight gem or rock you can weigh for a given scale precision and the accuracy level you can expect. For example, the first line shows that for a scale with .01ct precision, and SG measurement accuracy within .15 SG then the stone must weight 0.33 carats or more. If the stone is a spessartite with 4.12SG then the SG measured will be between 3.97SG and 4.27SG. The accuracy improves alot as the weight of the stone increases. Once the stone weighs more than 1 carat, the accuracy goes above .05 SG so a spessartite SG measure will be between 4.07SG and 4.15SG.
Example
Scales
Minimum Stone Weight Required for Scale Precision (Down) & SG Accuracy (Across)
Scale Precision
in Carats Below:
Accuracy Level SG, Using Baseline SG of 3.75
.01.05 .10.15.20 .25.30.35.40 .45.50
100ct x .01ct Carat Scale.014ct1ct0.6ct0.33ct0.25ct0.14ct0.14ct0.11ct0.11ct0.10ct0.10ct
100g x .01g Gram Scale.0522ct4.62ct2.71ct1.69ct1.28ct0.94ct0.87ct0.80ct0.60ct0.60ct0.53ct
500g x .1g Gram Scale.1045ct11.54ct5.95ct4.04ct2.95ct2.27ct2.00ct1.59ct1.59ct1.32ct1.18ct
No Scale Available.5 205ct61.73ct31.74ct19.50ct15.40ct12.67ct11.29ct9.26ct7.91ct6.57ct5.75ct
No Scale Available1.0440ct120ct57ct44ct29ct18ct14ct11ct11ct7ct7ct

Scale Precision Checker: Choose the specific gravity, starting carat weight, the precision of your scale, the amount to increment the carat weight,and the desired accuracy level. Press the Change button. The checker below will use your inputs to build a chart showing 80 different calculations and measurements that reveal the expected accuracy of your scale.

Specific Gravity is caclculated by getting the air weight and the water weight into the formula AIR WEIGHT / (AIR WEIGHT - WATER WEIGHT). However, because we are testing accuracy we will choose one S.G. and a series of air weights then solve for the water weight that we expect will be "read" on the scale for each given air weight and S.G. Solve for the water weight as WATER WEIGHT = AIR WEIGHT / (AIR WEIGHT - S.G.). This is the exact measure of the water weight under ideal conditions. We use the given precision of your scale to show what the typical reading on your scale will be. That scale reading is used with the Air and SG inputs to recalc the S.G. under less than ideal conditions. The difference between the exact solution of the water weight and the scale reading of the water weight is the amount of error introduced by your scale.

Specific Gravity
Scale Precision (cts)
Start Weight (cts)
Increment (cts)
Acceptable Error(SG)


Given Given Calculated Test Measure Result   Given Given Calculated Test Measure Result
Air Weight S.G. Water Weight Scale Water Weight Reading Scale S.G. Scale S.G. Error   Air Weight S.G. Water Weight Scale Water Weight Reading Scale S.G. Scale S.G. Error
0.05 3.90 0.03717949 0.04 5.00 -1.10   2.10 3.90 1.56153846 1.56 3.89 0.01
0.10 3.90 0.07435897 0.07 3.33 0.57   2.15 3.90 1.59871795 1.60 3.91 -0.01
0.15 3.90 0.11153846 0.11 3.75 0.15   2.20 3.90 1.63589744 1.64 3.93 -0.03
0.20 3.90 0.14871795 0.15 4.00 -0.10   2.25 3.90 1.67307692 1.67 3.88 0.02
0.25 3.90 0.18589744 0.19 4.17 -0.27   2.30 3.90 1.71025641 1.71 3.90 0.00
0.30 3.90 0.22307692 0.22 3.75 0.15   2.35 3.90 1.74743590 1.75 3.92 -0.02
0.35 3.90 0.26025641 0.26 3.89 0.01   2.40 3.90 1.78461538 1.78 3.87 0.03
0.40 3.90 0.29743590 0.30 4.00 -0.10   2.45 3.90 1.82179487 1.82 3.89 0.01
0.45 3.90 0.33461538 0.33 3.75 0.15   2.50 3.90 1.85897436 1.86 3.91 -0.01
0.50 3.90 0.37179487 0.37 3.85 0.05   2.55 3.90 1.89615385 1.90 3.92 -0.02
0.55 3.90 0.40897436 0.41 3.93 -0.03   2.60 3.90 1.93333333 1.93 3.88 0.02
0.60 3.90 0.44615385 0.45 4.00 -0.10   2.65 3.90 1.97051282 1.97 3.90 0.00
0.65 3.90 0.48333333 0.48 3.82 0.08   2.70 3.90 2.00769231 2.01 3.91 -0.01
0.70 3.90 0.52051282 0.52 3.89 0.01   2.75 3.90 2.04487179 2.04 3.87 0.03
0.75 3.90 0.55769231 0.56 3.95 -0.05   2.80 3.90 2.08205128 2.08 3.89 0.01
0.80 3.90 0.59487179 0.59 3.81 0.09   2.85 3.90 2.11923077 2.12 3.90 0.00
0.85 3.90 0.63205128 0.63 3.86 0.04   2.90 3.90 2.15641026 2.16 3.92 -0.02
0.90 3.90 0.66923077 0.67 3.91 -0.01   2.95 3.90 2.19358974 2.19 3.88 0.02
0.95 3.90 0.70641026 0.71 3.96 -0.06   3.00 3.90 2.23076923 2.23 3.90 0.00
1.00 3.90 0.74358974 0.74 3.85 0.05   3.05 3.90 2.26794872 2.27 3.91 -0.01
1.05 3.90 0.78076923 0.78 3.89 0.01   3.10 3.90 2.30512821 2.31 3.92 -0.02
1.10 3.90 0.81794872 0.82 3.93 -0.03   3.15 3.90 2.34230769 2.34 3.89 0.01
1.15 3.90 0.85512821 0.86 3.97 -0.07   3.20 3.90 2.37948718 2.38 3.90 0.00
1.20 3.90 0.89230769 0.89 3.87 0.03   3.25 3.90 2.41666667 2.42 3.92 -0.02
1.25 3.90 0.92948718 0.93 3.91 -0.01   3.30 3.90 2.45384615 2.45 3.88 0.02
1.30 3.90 0.96666667 0.97 3.94 -0.04   3.35 3.90 2.49102564 2.49 3.90 0.00
1.35 3.90 1.00384615 1.00 3.86 0.04   3.40 3.90 2.52820513 2.53 3.91 -0.01
1.40 3.90 1.04102564 1.04 3.89 0.01   3.45 3.90 2.56538462 2.57 3.92 -0.02
1.45 3.90 1.07820513 1.08 3.92 -0.02   3.50 3.90 2.60256410 2.60 3.89 0.01
1.50 3.90 1.11538462 1.12 3.95 -0.05   3.55 3.90 2.63974359 2.64 3.90 0.00
1.55 3.90 1.15256410 1.15 3.88 0.02   3.60 3.90 2.67692308 2.68 3.91 -0.01
1.60 3.90 1.18974359 1.19 3.90 0.00   3.65 3.90 2.71410256 2.71 3.88 0.02
1.65 3.90 1.22692308 1.23 3.93 -0.03   3.70 3.90 2.75128205 2.75 3.89 0.01
1.70 3.90 1.26410256 1.26 3.86 0.04   3.75 3.90 2.78846154 2.79 3.91 -0.01
1.75 3.90 1.30128205 1.30 3.89 0.01   3.80 3.90 2.82564103 2.83 3.92 -0.02
1.80 3.90 1.33846154 1.34 3.91 -0.01   3.85 3.90 2.86282051 2.86 3.89 0.01
1.85 3.90 1.37564103 1.38 3.94 -0.04   3.90 3.90 2.90000000 2.90 3.90 0.00
1.90 3.90 1.41282051 1.41 3.88 0.02   3.95 3.90 2.93717949 2.94 3.91 -0.01
1.95 3.90 1.45000000 1.45 3.90 0.00   4.00 3.90 2.97435897 2.97 3.88 0.02
2.00 3.90 1.48717949 1.49 3.92 -0.02   4.05 3.90 3.01153846 3.01 3.89 0.01
2.05 3.90 1.52435897 1.52 3.87 0.03   4.10 3.90 3.04871795 3.05 3.90 0.00












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